A301647 a(n) = n^3 - (n mod 2).

0, 8, 26, 64, 124, 216, 342, 512, 728, 1000, 1330, 1728, 2196, 2744, 3374, 4096, 4912, 5832, 6858, 8000, 9260, 10648, 12166, 13824, 15624, 17576, 19682, 21952, 24388, 27000, 29790, 32768, 35936, 39304, 42874, 46656, 50652, 54872, 59318, 64000, 68920, 74088, 79506, 85184, 91124

Offset

1,2

Comments

a(n) is the circumference of the n X n X n grid graph for n > 1.

Links

Table of n, a(n) for n=1..45.

Eric Weisstein's World of Mathematics, Graph Circumference

Eric Weisstein's World of Mathematics, Grid Graph

Index entries for linear recurrences with constant coefficients, signature (3, -2, -2, 3, -1).

Formula

a(n) = (2 n^3 + (-1)^n - 1)/2.

a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5).

G.f.: 2*x^2*(4 + x + x^2)/((-1 + x)^4*(1 + x)).

Maple

seq(n^3-modp(n, 2), n=1..50); # Muniru A Asiru, Mar 25 2018

Mathematica

Table[n^3 - Mod[n, 2], {n, 20}]
Table[(2 n^3 + (-1)^n - 1)/2, {n, 20}]
LinearRecurrence[{3, -2, -2, 3, -1}, {0, 8, 26, 64, 124}, 20]
CoefficientList[Series[2 x (4 + x + x^2)/((-1 + x)^4 (1 + x)), {x, 0, 20}], x]

Prog

(GAP) List([1..50], n->n^3- n mod 2); # Muniru A Asiru, Mar 25 2018
(PARI) a(n) = n^3 - (n%2); \\ Altug Alkan, Mar 25 2018

Crossrefs

Cf. A137932 (circumference of n X n grid graph).

Sequence in context: A002901 A350163 A213769 * A050471 A088024 A296112

Adjacent sequences: A301644 A301645 A301646 * A301648 A301649 A301650

Keyword

nonn,easy

Author

Eric W. Weisstein, Mar 25 2018

Status

approved